THEOREM 7. IfK is reducible to L and K' to L', then K 0 L is reducible to K' 0 L'. THEOREM 8. For a direct sum I1 + 112 of abelian groups H1 and II2, A0(H11 + II2) is reducible to A0(1) 0 A0(II2). Together with Theorem 2 and the results for cyclic groups, these Theorems prove THEOREM 9. If 11 is a finitely generated abelian group, then any abelian homology or cohomology group A,(II) or Af(II, J...

The classification of short exact sequences of p-compact groups and of rational isomorphisms of not necessarily connected p-compact groups is discussed.

If m is Haar measure in G (normalized so that m(G) = 1) we consider the set function m'{E) = m{E). (E is the set of all x, # £ £ . ) Since m is a measure on G possessing all defining properties of m it follows from the uniqueness of Haar measure that ?n'(E) =m(E) for every measurable set E. In other words a is a measure preserving transformation of G; the purpose of this note is to investigate ...